Differential Quaternary Phase Shift Keying (DQPSK) is an advanced new modulation format that has received great attention as a promising candidate for high spectral efficiency optical networks operable in high-speed transmissions (43 Gbit/s and beyond). However, the generation and reception of DQPSK signals is quite complex, as several feedback signals have to be generated to stabilize the transmitter and receiver, respectively.
In the following, a quick overview of the DQPSK generation and reception will be given for a better understanding of the invention, starting from an explanation of the PSK and QPSK modulation schemes.
Phase shift keying (PSK) is a digital modulation scheme for transmitting data by modulating the phase of a reference signal (carrier wave). Each of the phases is assigned a unique pattern of binary bits, in the following referred to as “symbol”, represented by that particular phase. In QPSK, the symbols are arranged equally spaced around a circle in the complex plane, each symbol corresponding to a pattern of two bits (“dibits”: “00”, “10”, “01” and “11”) as shown in FIG. 2a. In Differential Phase Shift Keying (DPSK), information is not directly encoded in the phase of the symbols, but in their phase difference. Therefore, in the DQPSK modulation scheme the symbols of FIG. 2a are encoded in a pulse phase difference of π/4, 3/4 π, −3/4 π, −π/4, respectively.
Although QPSK (and consequently DQPSK) can be viewed as a quaternary modulation, it is easier to see it as two independently modulated quadrature carriers. The even (odd) bits are then used to modulate the in-phase component of the carrier, while the odd (even) bits are used to modulate the quadrature-phase component of the carrier. Therefore, for generating a DQPSK signal, a binary bit stream has to be divided into two sequences corresponding to the in-phase and quadrature-phase components, respectively, such that the generation of a DQPSK modulated signal is more difficult compared to classical modulation schemes as e.g. On-Off Keying (OOK).
A fiber optical transmission system 1 for DQPSK-modulated optical signals shown in FIG. 1 has a pre-coder 2 for pre-coding a binary bit stream by generating the two sequences described above and forming two corresponding electrical modulation signals. These are provided to a transmitter 3 for generation of a DQPSK-modulated optical signal therefrom. The optical signal is then transmitted via a fiber line 4 to a receiver 5 which demodulates the DQPSK-modulated optical signal by reconstructing the in-phase and quadrature-phase components.
The following description will be focused on the transmitter 3 and receiver 5, as the pre-coding performed in the pre-coder 2 is of minor relevance for the invention and its mode of functioning is well-known to the person skilled in the art.
The DQPSK transmitter 3 of FIG. 1 is shown in greater detail in FIG. 3a and comprises a laser source 6 (laser diode) for generating an optical carrier signal, an optical splitter 7 for splitting the optical carrier signal into a first and second branch 8a, 8b with equal intensities, a first Mach-Zehnder Modulator (MZM) 9 in the first branch 8a, a second Mach-Zehnder Modulator 10 and an optical π/2 phase shifter 11 in the second branch 8b, and a signal combiner 7′ to produce a single DQPSK output signal from the optical signals of the two branches 8a, 8b. The first and second MZMs 9, 10 are operated as phase modulators and are driven each with an electrical modulation signal uk, vk corresponding to the in-phase and quadrature-phase sequences as described above. The electrical signals are provided with a data rate of 20 Gbit/s each, leading to an overall data rate of the optical signal of 40 Gbit/s.
In the transmitter 3, two imperfections have been pointed out: bias deviations of the Mach-Zehnder Modulators 9, 10 used as phase modulators and phase shift errors of the π/2 phase shifter 11, both of which will be described in greater detail below.
For modulating the optical carrier signal with the electrical modulation signals uk, vk, the Mach-Zehnder Modulators 9, 10 being simple two-wave interferometers are driven with an electrical drive voltage leading to a sinusoidal transfer function as shown in FIG. 4. When working properly, a bias voltage of the MZMs 9, 10 is set at the minimum of transmission of the interferometer such that the electrical drive for +/−Vπ, respectively, correspond to two adjacent maximum transmission points, as is the case for the solid curve of FIG. 4. Then a high bit rate signal is applied which is centred around 0 V and has a 2 Vπ amplitude. However, if the bias voltage is not adjusted properly, a bias deviation ΔV may occur, leading to a shift of the transmission curve such that the maximum optical transmission is no longer attained for +/−VπV but for a higher voltage, as is the case for the dashed curve in FIG. 4.
The bias deviation ΔV, defined as a shift of the bias voltage from its proper value, leads to a modification of the symbol constellation by moving them from their ideal positions in the complex plane as shown by the arrows in FIG. 2b. A bias deviation in the MZM 9 of the first branch 8a shifts the symbols horizontally whereas a bias deviation in the MZM 10 of the second branch 8b containing the π/2 phase shifter 11 shifts symbols vertically (only the first case being shown in FIG. 2b). In both cases, symbols are closer to each other than in the idealistic case, such that back-to-back sensibility is lower.
The modification due to the bias deviation leads to an amplitude reduction in the DQPSK modulated signal as well as to phase errors, as modulated phases are not equal to 0 and π/2, see the time domain representation of FIG. 10a for an optical signal with a bias deviation equal to π/10, wherein the amplitude of the optical power and phase are represented by a solid and dashed line, respectively. The amplitude level of the modified signal is reduced compared to the ideal case, as the interferences of the signals from the two branches 8a, 8b in the combiner 7′ of FIG. 3a are not totally constructive. Furthermore, some artefacts (spikes etc.) appear in the phase and amplitude curves as the maximum transmission is not centred on voltages −Vπ and +Vπ, respectively.
The degradation of the performance of an optical transmission system caused by the bias deviation can be gathered from FIG. 11a, showing the Q-factor penalty (solid line) and output power deviation (dashed line) measured in dB in dependence of the bias deviation for an optical signal-to-noise ratio (OSNR) of 14.5 dB. It can be gathered from FIG. 11a that even though system performance is not strongly affected for low bias deviations, large penalties are caused for higher deviations, leading to a 1 dB penalty for a deviation of 0.6 rad. Therefore, it is mandatory to find a way of reducing the bias deviations in the MZMs 9, 10 for stabilizing the transmitter 3 of FIG. 3a. 
Furthermore, the DQPSK transmitter 3 of FIG. 3a has to be stabilized with respect to impairments caused by the π/2 phase shifter 11. If the phase shift of the phase shifter 11 is not equal to π/2, interferences in the optical combiner 7′ or differential interferences at the demodulation part of a subsequent receiver are no more fully constructive or destructive. As can be gathered from FIG. 2c, representing the DQPSK symbols in the complex plane, a phase shift error leads to a dissymmetry in the DQPSK constellation resulting in different distances between the symbols, thus leading to different amplitude levels of the DQPSK optical signals generated in the transmitter 3, as can be gathered from FIG. 10b showing a time domain representation of an optical signal for a phase shift error of π/10. The main impairment of the π/2 phase shift error is the imperfection of interferences in the optical combiner 7′ at the output of the transmitter 3 of FIG. 3a. As a result, in addition to a first (normalized) power amplitude level 16, there is a second amplitude level 17 in the DQPSK optical signal (both marked by circles in FIG. 10b) such that detection at the receiver 5 of FIG. 1 is penalized. This is especially serious when using differential interferences for the demodulation, as the imperfect interferences between consecutive pulses affect system performances, as shown in FIG. 11b representing the Q-factor (solid line) which is penalized by a phase shift error at the transmitter, such that a 1 dB penalty is obtained for a 0.3 rad (corresponding to π/10) phase shift error.
In addition to the impairments of the transmission system 1 of FIG. 1 which are due to the transmitter 3 and have been described above, there are further impairments due to the receiver 5 shown in greater detail in FIG. 5a. 
The receiver 5 comprises a splitter 30 for splitting a received DQPSK optical signal in two equal parts, each of which is introduced to one of two branches 31a, 31b. In the following, only the components in the first branch 31a will be described in detail, like components of the second branch 31b being assigned primed reference numerals. The first branch 31a comprises a differential interferometer 32 for making two consecutive pulses interfere together and is followed by a balanced receiver 33. The differential interferometer 32 splits the optical signal into a first and second branch 36a, 36b, the first of which comprises a time delay 34, the second of which comprises phase shifter 35 with a nominal phase shift of +π/4. Both branches are recombined at the output of the interferometer 32 and split again before being introduced to photodiodes in respective branches of the differential receiver 33, transforming the two optical input signals of the photodiodes into one electrical output signal.
The second branch 31b differs from the first branch 31a only in that the phase shifter 35′ generates a nominal phase shift of −π/4 instead of +π/4. The total phase difference between the two phase shifters 35, 35′ of π/2 is the reason why the balanced receiver 33 of the first branch 31a decodes the in-phase components Ik of the DQPSK optical signal, whereas the balanced receiver 33′ of the second branch 33′ decodes the quadrature-phase components Qk.
The main impairment in the DQPSK receiver 5 described above consists in a phase shift which is not equal to π/4, resulting in a multi-level eye-diagram and lower sensibility at detection. This phase shift error may be due to the following origins: laser detuning, imperfections from the π/4 phase shifter, or a time delay T not equal to one bit time T.
All there causes can be summed up in a phase term Δφ:Δφ=Δφπ/4shift+2πΔvlaserT+2πΔTv0,wherein:Δφπ/4 is the phase shifter mismatchingΔvlaser is the laser detuning from its central wavelength v0 ΔT is the bit time delay error
In the following, the term “phase shift error” designates the phase term Δφ which is due to all the imperfections described above.
As is the case with the phase shift error of the transmitter, phase shift mismatching in the receiver also leads to imperfect interferences and consequently to a 4-level eye-diagram, i.e. 4 different amplitude levels. The time domain representation of the normalized amplitude of the voltage of the electrical signal at the output of the balanced receiver 33 is shown in FIG. 10c for the ideal case (solid line) and a phase shift error equal to π/10 (dashed line). It is remarkable that variations from the ideal signal are about 50% of the normalized intensity value, such that four distinct levels appear in this case instead of two levels when the receiver is optimized. Consequently, a logical “1” which should be encoded with a nominal amplitude level of 1.0 is encoded in two different amplitude levels, the first one 18 equal to 0.7, the second one 19 equal to 1.2.
As expected, FIG. 11c shows that the tolerance to phase shift error measured as Q-factor penalty (in dB) at the receiver side is very low: 1 dB is obtained for ±π/40 (solid line). For comparison, a phase shift equal to π/40 corresponds to Δvlaser=500 MHz. Concerning a laser source, usual wavelength instability is around 0.01 nm, i.e. 1.2 GHz.
In summary, the transmitter as well as the receiver have to be stabilized in order to counteract the impairments illustrated above. Feedback signals have to be found for this purpose from which appropriate bias signals for the Mach-Zehnder modulators and phase shifters can be generated. The best prior art solution is to set modulator (transmitter) and demodulator (receiver) by using the Bit Error Rate (BER) as a feedback signal. The idea of this solution is to find optimal settings by minimizing the BER. However, the disadvantage of this solution for transmitter and receiver settings is the cost of BER monitoring, being a rather complex algorithm. Furthermore, the BER is monitored at the receiver side which may be located several hundreds of kilometers away from the transmitter.